You can't opt-out of server-side tracking. They could easily architect the app to require a round-trip to the server on every call (this is how typical early web apps worked). In that case you really don't have an option to object.

Does that bother you too? (A service recording your usage of it)

Why is measuring on the client-side different from measuring on the server-side?

The difference is that server-side tracking doesn't track my clicks, scrolling, mouse moves or if I mistakingly type or paste some personal data (e.g. password) into some text field.

Server-side tracking is much more controllable in what and when the information is sent, instead of essentially having Telescreen[1] websites.

[1]: https://en.wikipedia.org/wiki/Telescreen

The privacy trade-offs of pulling the info off a website are simple and well-understood.

The trade-offs of a page that keeps pinging a mothership with every mouse wiggle are less comfortable.

The trade-offs of a page streaming out user's activity to a dedicated service are even more troublesome.